Numerical Methods For Viscosity Solutions And Applications

Author : Maurizio Falcone,Charalampos Makridakis
Publisher : World Scientific
Page : 256 pages
File Size : 50,8 Mb
Release : 2001
Category : Mathematics
ISBN : 981279980X

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Numerical Methods for Viscosity Solutions and Applications by Maurizio Falcone,Charalampos Makridakis Pdf

Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.

Author : Anonim
Publisher : Unknown
Page : 3 pages
File Size : 54,8 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:255947501

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Numerical Methods for Viscosity Solutions and Applications by Anonim Pdf

Author : Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Publisher : Springer
Page : 316 pages
File Size : 47,8 Mb
Release : 2013-05-24
Category : Mathematics
ISBN : 9783642364334

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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov Pdf

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Author : Martino Bardi,Italo Capuzzo-Dolcetta
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 42,6 Mb
Release : 2009-05-21
Category : Science
ISBN : 9780817647551

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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by Martino Bardi,Italo Capuzzo-Dolcetta Pdf

This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.

Author : Dante Kalise,Karl Kunisch,Zhiping Rao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 261 pages
File Size : 52,6 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9783110542714

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Hamilton-Jacobi-Bellman Equations by Dante Kalise,Karl Kunisch,Zhiping Rao Pdf

Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme

Author : Wendell H. Fleming,Halil Mete Soner
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 46,9 Mb
Release : 2006-02-04
Category : Mathematics
ISBN : 9780387310718

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Controlled Markov Processes and Viscosity Solutions by Wendell H. Fleming,Halil Mete Soner Pdf

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Author : Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 47,5 Mb
Release : 1999-06
Category : Mathematics
ISBN : 0817640290

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Stochastic and Differential Games by Martino Bardi,T.E.S. Raghavan,T. Parthasarathy Pdf

The theory of two-person, zero-sum differential games started at the be­ ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton­ Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe­ sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv­ ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po­ sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.

Author : J. Necas
Publisher : Routledge
Page : 188 pages
File Size : 46,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351425865

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Partial Differential Equations by J. Necas Pdf

As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.

Author : Maurizio Falcone,Roberto Ferretti
Publisher : SIAM
Page : 331 pages
File Size : 49,7 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9781611973044

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Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by Maurizio Falcone,Roberto Ferretti Pdf

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.

Author : Maurizio Falcone,Roberto Ferretti
Publisher : SIAM
Page : 331 pages
File Size : 54,6 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9781611973051

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Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by Maurizio Falcone,Roberto Ferretti Pdf

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.

Author : Martino Bardi,Michael G. Crandall,Lawrence C. Evans,Halil M. Soner,Panagiotis E. Souganidis
Publisher : Springer
Page : 266 pages
File Size : 51,5 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 3662205971

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Viscosity Solutions and Applications by Martino Bardi,Michael G. Crandall,Lawrence C. Evans,Halil M. Soner,Panagiotis E. Souganidis Pdf

The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.

Author : Dale R. Durran
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 49,8 Mb
Release : 2010-09-14
Category : Mathematics
ISBN : 9781441964120

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Numerical Methods for Fluid Dynamics by Dale R. Durran Pdf

This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Author : Stanislaw Sieniutycz,Jacek Jezowski
Publisher : Elsevier
Page : 771 pages
File Size : 46,6 Mb
Release : 2009-05-06
Category : Technology & Engineering
ISBN : 9780080914428

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Energy Optimization in Process Systems by Stanislaw Sieniutycz,Jacek Jezowski Pdf

Despite the vast research on energy optimization and process integration, there has to date been no synthesis linking these together. This book fills the gap, presenting optimization and integration in energy and process engineering. The content is based on the current literature and includes novel approaches developed by the authors. Various thermal and chemical systems (heat and mass exchangers, thermal and water networks, energy converters, recovery units, solar collectors, and separators) are considered. Thermodynamics, kinetics and economics are used to formulate and solve problems with constraints on process rates, equipment size, environmental parameters, and costs. Comprehensive coverage of dynamic optimization of energy conversion systems and separation units is provided along with suitable computational algorithms for deterministic and stochastic optimization approaches based on: nonlinear programming, dynamic programming, variational calculus, Hamilton-Jacobi-Bellman theory, Pontryagin's maximum principles, and special methods of process integration. Integration of heat energy and process water within a total site is shown to be a significant factor reducing production costs, in particular costs of utilities for the chemical industry. This integration involves systematic design and optimization of heat exchangers and water networks (HEN and WN). After presenting basic, insight-based Pinch Technology, systematic, optimization-based sequential and simultaneous approaches to design HEN and WN are described. Special consideration is given to the HEN design problem targeting stage, in view of its importance at various levels of system design. Selected, advanced methods for HEN synthesis and retrofit are presented. For WN design a novel approach based on stochastic optimization is described that accounts for both grassroot and revamp design scenarios. Presents a unique synthesis of energy optimization and process integration that applies scientific information from thermodynamics, kinetics, and systems theory Discusses engineering applications including power generation, resource upgrading, radiation conversion and chemical transformation, in static and dynamic systems Clarifies how to identify thermal and chemical constraints and incorporate them into optimization models and solutions

Author : Stanislaw Sieniutycz,Jacek Jezowski
Publisher : Newnes
Page : 821 pages
File Size : 40,8 Mb
Release : 2013-02-14
Category : Technology & Engineering
ISBN : 9780080982274

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Energy Optimization in Process Systems and Fuel Cells by Stanislaw Sieniutycz,Jacek Jezowski Pdf

Energy Optimization in Process Systems and Fuel Cells, Second Edition covers the optimization and integration of energy systems, with a particular focus on fuel cell technology. With rising energy prices, imminent energy shortages, and increasing environmental impacts of energy production, energy optimization and systems integration is critically important. The book applies thermodynamics, kinetics and economics to study the effect of equipment size, environmental parameters, and economic factors on optimal power production and heat integration. Author Stanislaw Sieniutycz, highly recognized for his expertise and teaching, shows how costs can be substantially reduced, particularly in utilities common in the chemical industry. This second edition contains substantial revisions, with particular focus on the rapid progress in the field of fuel cells, related energy theory, and recent advances in the optimization and control of fuel cell systems. New information on fuel cell theory, combined with the theory of flow energy systems, broadens the scope and usefulness of the book Discusses engineering applications including power generation, resource upgrading, radiation conversion, and chemical transformation in static and dynamic systems Contains practical applications of optimization methods that help solve the problems of power maximization and optimal use of energy and resources in chemical, mechanical, and environmental engineering

Author : Todor Boyanov,Stefka Dimova,Krassimir Georgiev,Geno Nikolov
Publisher : Springer
Page : 732 pages
File Size : 42,5 Mb
Release : 2007-05-15
Category : Computers
ISBN : 9783540709428

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Numerical Methods and Applications by Todor Boyanov,Stefka Dimova,Krassimir Georgiev,Geno Nikolov Pdf

This book constitutes the thoroughly refereed post-proceedings of NMA 2006 held in Borovets, Bulgaria. Coverage in the 84 revised full papers includes numerical methods for hyperbolic problems, robust preconditioning solution methods, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, and large-scale computations in environmental modeling.